Jakub,
Your attachment 8762570[details] font-size-demo.zip is a compressed file of some 20 files each with many KiloBytes. This is not best, not ideal.
Reduced test:
http://www.gtalbot.org/BugzillaSection/Bug1279948-font-size-not-inherited-in-table-quirks-mode.html
From quirks.css at line 51 of chrome/toolkit/res/quirks.css
table {
text-align: start;
white-space: normal; /* compatible with IE & spec */
line-height: normal;
/* Quirk: cut off all font inheritance in tables except for family. */
font-size: initial;
font-weight: initial;
font-style: initial;
font-variant: initial;
}
Chances are IE10+ and Edge also do the same thing. I am almost certain that this used to be a bug also in IE some 15 years ago: font-size not inherited into table in quirks mode.
Fixing Table Inheritance in Quirks Mode
https://developer.mozilla.org/en-US/docs/Fixing_Table_Inheritance_in_Quirks_Mode
The comment in the user agent style sheet at line 56 fits perfectly this bug report. This is an nth reason as to why no one should be triggering backward-compatible "quirks" rendering mode in any browser and should always use a valid, recommended doctype declaration triggering web-standards-compliant rendering mode.
Resolving as INVALID

I just check that 'Pinger - localhost.html' from the zip and it has a doctype declaration... so I am confused now...
Re-setting bug to UNCONFIRMED
Jakub,
We need a reduced test from your zipfile. Your zipfile has 22 files and over 1 Mbyte of code. When I open, I can not find that label address you mentioned. I see that the page has iframes and so, my previous comments could still be relevant here.